Решите систему уравнений: 2x+y=7; x^2-xy=6.

\[\left\{ \begin{matrix} 2x + y = 7\ \ \\ x^{2} - xy = 6 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} y = 7 - 2x\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ x^{2} - x(7 - 2x) = 6 \\ \end{matrix} \right.\ \]

\[x^{2} - 7x + 2x^{2} - 6 = 0\]

\[3x^{2} - 7x - 6 = 0\]

\[D = 49 + 72 = 121\]

\[x_{1} = \frac{7 + 11}{6} = \frac{18}{6} = 3;\ \]

\[x_{2} = \frac{7 - 11}{6} = - \frac{4}{6} = - \frac{2}{3};\]

\[y_{1} = 7 - 2 \cdot 3 = 1;\]

\[y_{2} = 7 - 2 \cdot \left( - \frac{2}{3} \right) = 7 + \frac{4}{3} = 8\frac{1}{3}.\]

\[Ответ:(3;1);\left( - \frac{2}{3};8\frac{1}{3} \right).\]